• محدودیت زمان: ۴ ثانیه
• محدودیت حافظه: ۳۲ مگابایت

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In a two-dimensional coordinate plane, there are N distinct points given as input, specified by their coordinates \((x_i, y_i)\) for \(i = 1, 2, ..., N\). Your task is to develop a program that computes the number of unique Orthogonal (right) triangles that can be formed by selecting any three of the provided points.

An Orthogonal triangle is a triangle in which one of the angles measures exactly 90 degrees.

Input

The first line of input contains an integer N, the number of points.

Each of the following N lines contains the coordinates of one point, two integers \((x_i, y_i)\) separated by a space. No two points will be located at the same coordinates.

Output

Output the number of Orthogonal triangles.

Constrints

• \(3 \leq N \leq 1500 \)
• \(-10^9 \leq x_i,y_i \leq 10^9 \)

Sample Test Data

input 1

5
1 1
1 0
0 0
-1 0
-1 1

input 2

7